Result clarifies role of measurement in the Heisenberg Uncertainty Principle.

One of the most important—and famous—results in quantum mechanics is the Heisenberg Uncertainty Principle (HUP). What is less known (at least to non-physicists) is that the HUP exists in two versions. Werner Heisenberg's original formulation stated that the act of measurement disturbs a physical system, placing strong constraints on (for example) the simultaneous measurement of both the position and momentum of a particle. A more mathematically rigorous version places inherent limits on the measurement of physical quantities—independent of whether any measurement is actually performed.

While it is often assumed that these different formulations are the same, recent theoretical results have shown the original Heisenberg measurement-based version is incomplete.

A possible violation of the original HUP has been realized experimentally by a group at the University of Toronto. Lee A. Rozema and colleagues performed a series of polarization measurements on entangled photons to determine the degree of disturbance in the system. The two possible polarization states of a photon are complementary in a quantum mechanical sense, meaning they cannot be simultaneously measured to arbitrary precision. If the original HUP is the correct one, then the physical act of measuring the polarization in one orientation will perturb the photon, affecting subsequent measurements. The researchers found that, while the later version of the HUP held, the Heisenberg HUP was violated. This result is an explicit verification that the HUP is due to intrinsic uncertainty in quantum systems rather than the effect of introducing macroscopic measurement apparatus.

Complementary physical quantities play an important role in quantum physics. The most famous pair is position and momentum: pinpointing a particle's position means its state of motion is indeterminate. Heisenberg proposed that the act of measurement itself was responsible for the indeterminacy: using a photon of sufficient energy to locate the particle would give it a kick, making its momentum unpredictable. However, later more rigorous derivations showed that the HUP—while still concerned with the measurement of physical quantities—didn't require a specific measurement to be performed. Instead, the HUP was a statement of the intrinsic limitation of any measurement that could be taken, without needing to do an experiment. For future reference, I'll refer to the more advanced version of the HUP as the modern Heisenberg Uncertainty Principle, or MHUP.

While this distinction may seem academic, it's not. An earlier paper by Masanao Ozawa showed that Heisenberg's formulation was too stringent, which left room for sufficiently weak measurements to violate it. In other words, Ozawa's calculation showed that real measurements could violate Heisenberg's original formulation of the HUP, yet still be consistent with the MHUP. (Confession: I've conflated the two versions of the HUP when I taught the subject in the past. I'm not alone: the three quantum physics textbooks I have on my shelf do the same thing.)

The Canadian researchers used another set of complementary physical quantities instead of position and momentum: the polarization states of a photon. Precision measurement of polarization along one axis (for example) means that the measurement along another perpendicular axis is indeterminate. Not only is light polarization easier to manipulate than position or momentum, the researchers were able to use the technology of quantum entanglement—which nearly always uses photon polarization—to construct their experiment.

The authors constructed a quantum circuit, producing two photons with opposite (but unknown) polarization states. The two photons traveled down separate paths, but because their states were entangled, a measurement taken along one path revealed the state of the photon on the other path. The quantum state was measured using polarizing beam splitters (PBSs), which select photons to travel in different directions based on their polarization state. By selecting particular polarization configurations on the second photon of the entangled pair, the researchers were able to determine if the PBS had changed the state of the system—a direct test of Heisenberg's original HUP formulation.

They found that the data supported the Ozawa version of the HUP formula, with its less stringent effects from measurement perturbation. While the results were not completely in agreement with the theoretical calculation, the authors believed this is due to the imperfect nature of the initial preparation of the entangled photons. However, the results did not come close to agreement with the original Heisenberg HUP formulation.

The use of weak measurements allowed the researchers to quantify the amount of disturbance the experimental apparatus introduced. In that way, they could rule out Heisenberg's idea that it was the measurement itself that led to uncertainty. These results help clarify the role of measurement in quantum mechanics.

This is pretty awesome. If I read this right, it's not that our measurements introduce uncertainty into the results, it's that the state of reality is inherently uncertain. This is, indeed, not merely an academic distinction. It means that our typical obsession with certainty is just not going to be satisfied. Certainty is not on offer. We must be content with confidence.

In QM everything is a particle and a wave. For, say, sound waves, you might want to determine the intensity of a frequency at a particular point in time. For example, what note (or Hz) is the violin playing at exactly 1 second into the sample below:

The smaller you make the time window, the fewer oscillations you can use to determine the frequency--you lose decimal places. But you gain time precision as you shrink the window from say 1-2 seconds, to 1-1.5 seconds, to 1-1.25 seconds, etc.

You can't have precision in both frequency and time though.

That this is intrinsic in QM seems to be due to the fact that it's intrinsic to wave systems in general, IMHO.

OK, so haven't I read that one of the benefits of quatum computing is the fact that you could always tell if your data had been snooped (observed)? This result would seem to blow that out of the water - if I'm comprehending this article correctly (an assumption with a high probability of falseness).

Okay. That makes more sense now. I hadn't been aware that there were two different versions of HUP, and I was puzzled that something purported to violate HUP didn't get any coverage in any of the other sites I follow.

So, HUP and revised HUP work, but this is a corner case where the old model breaks? Kinda like how Newtonian physics is great for predicting orbits, but Mercury is a corner case where it breaks, requiring GR to fix it?

In "Hidden Reality" B. Greene gives an example of a photo taken of a flying bird: with longer exposure you get a sense of its movement, but fine details of the bird itself get blurred, with short exposure you get great details of the bird, but no sense of movement.

I am pretty sure there are many varieties of uncertainty principles, similar to how there are many ways to put theories of quantum mechanics or non-commutativity. In the latter case classical time-energy differs from, say, position-momentum with the former being global symmetries. (I believe, should follow from Noether's theorems but I haven't studied those.) [ http://en.wikipedia.org/wiki/Uncertainty_principle ]

I think Heisenberg's observer effect version was early replaced by inherent uncertainty of wavefunctions as demonstrated by Fourier analysis. (The subject maps nicely to Fourier-Fourier distribution theory, if you like math.)

At the very least weak measurements all by themselves show that the observer effect hypothesis is erroneous.

Aurich wrote:

There oughta be a law against an editor asking me for an image for a quantum story first thing in the morning.

It's the Coffee Uncertainty Principle (CUP): I'm too tired to remember, did I or did I not have have coffee!?

Or in other words, you can't mix science and belief. It is the SCP (Science Certainty Principle).

drumhellar916 wrote:

So, HUP and revised HUP work, but this is a corner case where the old model breaks? Kinda like how Newtonian physics is great for predicting orbits, but Mercury is a corner case where it breaks, requiring GR to fix it?

I believe the paper compares the factorization of Heisenberg's UP vs Robertson's UP in which HUP comes out as a term.

It is kind of reminiscent, but perhaps more like how cartoons handle gravity vs classical mechanics fall trajectories.

Yes, this is a sensible result. The uncertainty principle has more to do with the fact that it is nonsensical to ask about the exact position and momentum of a wave which inherently has an extent. What we think of as a position of a particle has to do with when it interacts with another particle as opposed to a true position.

What I am still trying to figure out is how this relates to entanglement and “action at a distance”.

This is pretty awesome. If I read this right, it's not that our measurements introduce uncertainty into the results, it's that the state of reality is inherently uncertain. This is, indeed, not merely an academic distinction. It means that our typical obsession with certainty is just not going to be satisfied. Certainty is not on offer. We must be content with confidence.

You're right, this is pretty awesome stuff. This round of experiments confirms not only the fundamental uncertainty of the universe, but that the universe is uncertain even when not measured (part of the MHUP).

What really blows my mind about that is the potential implications for the related subject of the observer effect. If it's not some sort of measurement that does the job, then what in blazes collapses Eigenfunctions? Or in other words: does this mean that the cat was set in a dead state (or alive) even before we opened the box?

Yes yes, but what about the cat? Is it slightly more alive or more weakly dead?

Since it's inherently alive and dead, and it's not just a measurement problem: you're somewhat less responsible for the cat's possible death than you would be if your measurement affected the state of the cat.

Yes yes, but what about the cat? Is it slightly more alive or more weakly dead?

Since it's inherently alive and dead, and it's not just a measurement problem: you're somewhat less responsible for the cat's possible death than you would be if your measurement affected the state of the cat.

Why did I have to mention the cat? Forget the cat. Why did Schrödinger have to use a cat? Cat's are too fascinating; why not a rodent? No rodent would distract people from the importance of collapsing Eigenfunctions - was it an intentional diversionary tactic? Did Schrödinger expect the existential quandary we'd be left with in the absence of an observer effect and give us a cat for distraction or company? I smell a rat.

Perhaps Eigenfunction determination is one of God's little infinite jobs - sending out lots of divine blow-darts to pop all but the real determination state... but I'd sure like to know how it's done.

PS - I've never been worried about assigning responsibility for the cat's death - since it's a science thing I always assumed they killed the cat at the end on general principal. Since it's a physics thing, they probably don't even need to worry the IRB for anything less than a 10% chance of destroying the planet (if the theoretical physicists even know what an IRB is).

Yes yes, but what about the cat? Is it slightly more alive or more weakly dead?

Since it's inherently alive and dead, and it's not just a measurement problem: you're somewhat less responsible for the cat's possible death than you would be if your measurement affected the state of the cat.

Why did I have to mention the cat? Forget the cat. Why did Schrödinger have to use a cat? Cat's are too fascinating; why not a rodent? No rodent would distract people from the importance of collapsing Eigenfunctions - was it an intentional diversionary tactic? Did Schrödinger expect the existential quandary we'd be left with in the absence of an observer effect and give us a cat for distraction or company?

Yes, in fact. The entire gedankenexperiment is meant to be absurd, proving the absurdity of quantum mechanics. Too bad for Schrodinger it turned out to be right after all.

Yes yes, but what about the cat? Is it slightly more alive or more weakly dead?

Since it's inherently alive and dead, and it's not just a measurement problem: you're somewhat less responsible for the cat's possible death than you would be if your measurement affected the state of the cat.

Why did I have to mention the cat? Forget the cat. Why did Schrödinger have to use a cat? Cat's are too fascinating; why not a rodent? No rodent would distract people from the importance of collapsing Eigenfunctions - was it an intentional diversionary tactic? Did Schrödinger expect the existential quandary we'd be left with in the absence of an observer effect and give us a cat for distraction or company?

Yes, in fact. The entire gedankenexperiment is meant to be absurd, proving the absurdity of quantum mechanics. Too bad for Schrodinger it turned out to be right after all.

Except that the cat's state isn't determined per se by macroscopic observation.

Yes yes, but what about the cat? Is it slightly more alive or more weakly dead?

This isn't quite what this experiment is dealing with. Heisenberg's original interpretation of the uncertainty principal was that in order to measure something you had to somehow physically interact with the thing being measured. For example by analogy (and please don't take this too far or I'll look stupid(er?)), on a macro (and classical) scale one might determine the position of a baseball in a dark room by throwing a whole bunch of marbils all at once in the suspected path of the baseball and seeing which ones don't make it to the other side (i.e. are blocked by the baseball - like a shadow). This would allow you to locate the baseball at a particular time with precision, but all the marbils hitting the baseball would alter the path of the baseball, thus making its momentum uncertain. The baseball had both well defined position and momentum before the measurement, but measuring the position messed up the momentum. The original version of Heisenberg's principal is kind-of like that... In order to locate, say, an electron you might shine some sufficiently energetic photons on it, but when one of those photons interacts with the electron (thus locating it) it would cause the electron's original momentum to change and thus the original momentum would become unmeasurable with any precision. Locating the electron with more precision would require shorter wavelength (and thus higher energy) photons which would, upon interacting with it, more strongly effect the electron's momentum, thus further decreasing the precision with you may measure its original momentum.

The newer version holds that the uncertainty is somehow inherent in the thing being measured itself. You don't have to actually physically interact with the thing being measured for the uncertainty to exist.

As to Schrödinger's cat... what sep332 said. It's a somewhat different thing used to explore different interpretations of quantum mechanics (it was devised to show the seeming absurdity of the Copenhagen interpretation) and has a really badly (if at all?) defined sense of "measurement." I think that the Wikipedia entry is quite good.

P.S.

Quote:

(Confession: I've conflated the two versions of the HUP when I taught the subject in the past. I'm not alone: the three quantum physics textbooks I have on my shelf do the same thing.)

My original modern physics professor (back in the mists of time) taught both versions, sort of, and told us that he himself subscribed to Heisenberg's original version, but that it was probably wrong and that we should go by the newer version... except when listening to him or reading his textbook of course.

I took Quantum Mechanics a long time ago - about 1980. At the time, it seemed to me that the measurement impact was just a way to describe it - not the actual underlying mechanism.

Is it possible to set up an experiment where you can precisely set the two quantities that you are trying to measure? Then, you could pass this information to the observer and they could record -without observing. Would this violate MHUP or is it not even possible? My guess is that even if you could set up the experiment, you could not transmit the information to the observer.

While there are so many ways to skin a cat. The movie Battleship introduced another way of how those earth human accurately pin pointing the unpredictable position-momentum of the exact locations of the aliens warships by using blocks of radar to track them. And if using even smaller blocks of radar it even predicts a much defined future positions of the objects. Heisenberg might have a more complex way of calcuating it in his older days, the principal method shown on this Battleship fictional movie and Heisenberg's should be the same. With the advance of our modern computer technology we can over turned Heisenberg's "pinpointing a particle's position means its state of motion is indeterminate." - A possibility.

But doesn't inherent uncertainty follow in any wavelike system from Fourier transformation? Any Fourier transformation pair will have that uncertainty due to the wave like nature of a system?

Yes, I recall it directly follows by mathematical derivation as a consequence of the momentum and position operators being defined in such a way that they are Fourier transforms of each other. There is a generalized Heisenberg relation for any pair of operators, I believe it goes:[Standard deviation of A][Standard deviation of B] >= (1/2)*Expectation value (AB-BA)

One of the interesting questions about this statistical distribution language of standard deviations and expectation values is whether this result, and the idea of a wavefunction distribution in general, is the actual reality for a single particle, or whether this is talking about an ensemble of similar particles and the spread amongst them. There's still some debate over this, though the former view is predominant.

One of the interesting questions about this statistical distribution language of standard deviations and expectation values is whether this result, and the idea of a wavefunction distribution in general, is the actual reality for a single particle, or whether this is talking about an ensemble of similar particles and the spread amongst them. There's still some debate over this, though the former view is predominant.

One of the interesting questions about this statistical distribution language of standard deviations and expectation values is whether this result, and the idea of a wavefunction distribution in general, is the actual reality for a single particle, or whether this is talking about an ensemble of similar particles and the spread amongst them. There's still some debate over this, though the former view is predominant.

No, discussions persist to this day, though as I said, the interpretation that the wavefunction describes the actual reality of a single particle is the predominant view. It's by no means unanimous, however, and the whole subject can be taught through the alternative lens. See "Ensemble Interpretation of QM" for example. For example, with the slit experiments, the famous interference patterns you see are only produced from a huge number of individual particles, and they are built up precise point by precise point. The fact that there are "interference patterns" resulting from a bunch of electrons (and other things as well) just as you'd see from a bunch of photons indicates there is something strange and interesting going on, however, to be perfectly precise, experimentally, no one has ever recorded "a single electron interfering with itself" / "going through both slits at once" as described in lay explanations.

You only see these sorts of effects built up in a composite fashion from a bunch of particles, point by point like some pointillist painting.

This is pretty awesome. If I read this right, it's not that our measurements introduce uncertainty into the results, it's that the state of reality is inherently uncertain. This is, indeed, not merely an academic distinction. It means that our typical obsession with certainty is just not going to be satisfied. Certainty is not on offer. We must be content with confidence.

You're right, this is pretty awesome stuff. This round of experiments confirms not only the fundamental uncertainty of the universe, but that the universe is uncertain even when not measured (part of the MHUP).

What really blows my mind about that is the potential implications for the related subject of the observer effect. If it's not some sort of measurement that does the job, then what in blazes collapses Eigenfunctions? Or in other words: does this mean that the cat was set in a dead state (or alive) even before we opened the box?

But that is the real question isn't it, what collapses the wave Eigenfunction.

I think there are a couple of answers that are oddly consistent, one is that measurement does, but it collapses it to a state consistent with the UP. Non weak measurements will force a particle into a certain state (if you trap is of a certain size, your particle can't be more uncertain in position than the trap size.)

I suspect the second answer is self-action, the same way interaction with your detector (trap) forces a particles state, so does the particles self action, the electron doesn't grow to the size of the universe for the same reason a galaxy doesn't. Likewise photons only accept certain configurations to self-propagate. Interesting point, I understand there is a relation between measured red shift and how QM would change a photons Eigenfunction over time.